Measuring and Improving Mixing Times with Image Analysis

Industrial engineers and others often characterize the performance of agitating impellers using total mixing time — the amount of time that it takes for a solution to reach a degree of homogeneity after a change, such as that caused by stirring. Mixing time can be an important parameter in comparing one agitation-inducing setup with another.

An indicator — bromocresol and water — is purple when basic and yellow when acidic, with the transition between the two the result of a fast reaction. Likewise, the addition of an acid, HCl, to a tank being mixed by an impeller makes visible classic radial discharge ring patterns. Courtesy of Philippe A. Tanguy, École Polytechnique de Montréal.However, there is no universally accepted method for determining the mixing time, partly because current techniques present researchers with two less-than-ideal choices: They can get an accurate but small view, or they can see the big picture with less accuracy. But thanks to image processing and analysis, researchers at École Polytechnique de Montréal have developed a better approach.

“Mixing time was determined by naked eye and a chronograph with a lot of subjectivity,” said Philippe A. Tanguy, a professor in the university’s chemical engineering department. “Now we have a reproducible method based on pixel analysis.” Others in the research group included graduate students François Cabaret and Sylvain Bonnot, and professor Louis Fradette.

On top is the setup, with lights shining through a tank to a digital camera. In the middle is the raw image data, as the purple solution turns yellow with the addition of an acid. On the bottom is the processed data, with the number of purple pixels counted as a way to show when mixing occurred. Courtesy of Philippe A. Tanguy.Mixing time typically has been determined by one of two types of techniques. The first is based on local measurement of conductivity, pH, fluorescence or other factors, with a change in the measured value tracking the degree of mixing. Such techniques are accurate but intrusive. They also determine the degree of mixing at only a given spot, which means that they cannot easily uncover dead zones or regions where fluids segregate. The second set involves global measurements, such as tracking color changes brought about by mixing. Such methods are not intrusive and can identify dead or segregated regions, but they are somewhat inaccurate.

For their new approach, the scientists began with a longtime method — a fast acid-based indicator reaction. In a demonstration, they used a solution of bromocresol or one of five other compounds in glucose as an indicator. With bromocresol, when the pH was <5.2, the solution was yellow; it was purple when the pH was >6.8. The other compounds underwent their own color changes as the pH changed over particular ranges.

Three similar impellers yield three different results. All are spun at the same rate and in the same fluid, but differences in design produce various mixing efficiencies. The impeller on the bottom, for example, is more efficient. With the analysis of captured digital video, that difference can be quantified. Reprinted with permission of the American Chemical Society.So, by injecting an acid into an alkaline bromocresol solution in a transparent tank, the investigators could see it change from purple to yellow. They chose this color evolution instead of its opposite for visibility reasons. “It is far easier and more reliable to detect purple unmixed zones in a yellow liquid than the opposite,” Tanguy said.

To this old idea they applied some new technology — a Sony video camera linked to a computer via an IEEE-1394 cable. As described in the July 4 issue of Industrial & Engineering Chemistry Research, the investigators illuminated the tank from one side with a set of lights and a diffuser and captured the color change in the solution as it occurred by placing the camera on the other side. They applied image processing and analysis to the video, using software they developed themselves.

Their analysis technique defined an area of interest and looked at the change of red, green and blue components in the area on a pixel-by-pixel basis. To determine when a pixel changed from purple to yellow, they set a threshold for either the red, green or blue elements of each. Therefore, they might allow the red and blue components to be any value in the full range of 0 to 255, while they used the green to track when a pixel changed from purple to blue. If the green value were anywhere from 0 to the threshold, the pixel would be classified as purple, but if the green component were anywhere from just above the threshold to 255, the pixel would be categorized as yellow. They set the threshold after collecting data and doing a preliminary analysis.

They tried the technique on three mixing systems of varying tank sizes, impeller geometries and impeller positions. They found that their method gave almost the same results for repeated runs under the same conditions and was largely immune to changes in illumination, provided that the color component used for threshold determination was not saturated. They used the technique to design an impeller that achieves better mixing results.

The technique does have its drawbacks. For example, it is limited by the spatial resolution of the camera. And it does not provide mixing versus depth information because the camera captures only two-dimensional data. However, those constraints do not bother Tanguy.

“Right now, we are satisfied with what we have. We are using the method to investigate other mixing systems — vessel-based and also in-line.”

The emission of light or other electromagnetic radiation of longer wavelengths by a substance as a result of the absorption of some other radiation of shorter wavelengths, provided the emission continues only as long as the stimulus producing it is maintained. In other words, fluorescence is the luminescence that persists for less than about 10-8 s after excitation.